|
|
|
||||||||||||||||
|
Raising Numbers to Various Powers | Rules of Exponents | Roots & Radicals | Signed Numbers & Roots | Rational & Irrational Numbers | Real & Imaginary Numbers | Finding Square Roots & Other Roots | Summary
Roots and Radicals
Just as it is necessary to raise numbers to powers in math, sometimes we are required to do the opposite, that is, to find the root of a number. The root of a number is the factor that multiplies out to give us the square or cube, or other power we are seeking. To show that we want to find the root of a number, we place it under the radical sign: For example, if we wanted to find the square root of 25, we would put 25 under the radical sign, like this... ...and the square root of 25 would be 5, since 5 x 5 = 25. To find the cube root of a number (or roots higher than cube roots), we would put a small sized number to the upper left outside the radical sign, to indicate what root we wanted. For example, the cube root of 343 would be expressed like this: And the cube root of 343 would be 7, since 7 x 7 x 7 = 343. To represent the fourth root of a number, the small upper left number would be four, like this: The fourth root of 1296 is 6, since 6 x 6 x 6 x 6 = 1296. So, what we have to remember is when we see a number placed under the radical sign its value is actually a root of the number. This means that:
Signed Numbers and Roots (top)The square root of a number can be either a positive or negative value. That is:
So, the square root of any positive number can be either a positive or negative root. And to carry that notion a step further, any positive number under a radical with an even numbered exponent can have either a positive or negative root. In finding 'roots' in the above examples, please note that each one turned out to be a whole number, without any remainder. What if you do get remainders when you calculate roots? Let's consider that now, and find out what to do about it. Then, we will also find out how to calculate roots. For an additional Practice Exercise on finding the square
root go to: Play the Tic Tac Toe Squares game dealing
with square roots by clicking on the math site link below:
|
||||||||||||||||
..and that
...and
that
because (+5) x (+5) = +25, and (-5) x (-5) = +25.